A Canonical Representation of Block Matrices with Applications to Covariance and Correlation Matrices

Ilya Archakov; Peter Reinhard Hansen

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arXiv · 2012.02698

A Canonical Representation of Block Matrices with Applications to Covariance and Correlation Matrices

Ilya Archakov·Peter Reinhard Hansen

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Abstract

We obtain a canonical representation for block matrices. The representation facilitates simple computation of the determinant, the matrix inverse, and other powers of a block matrix, as well as the matrix logarithm and the matrix exponential. These results are particularly useful for block covariance and block correlation matrices, where evaluation of the Gaussian log-likelihood and estimation are greatly simplified. We illustrate this with an empirical application using a large panel of daily asset returns. Moreover, the representation paves new ways to regularizing large covariance/correlation matrices, test block structures in matrices, and estimate regressions with many variables.

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BibTeX RIS

Ilya Archakov, Peter Reinhard Hansen. 2020-12-04. A Canonical Representation of Block Matrices with Applications to Covariance and Correlation Matrices. https://arxiv.org/abs/2012.02698

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